GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Oct 2018, 15:52

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# in how many ways can 9 identical balls be distributed among four baske

Author Message
TAGS:

### Hide Tags

Manager
Joined: 23 Sep 2016
Posts: 220
in how many ways can 9 identical balls be distributed among four baske  [#permalink]

### Show Tags

17 Mar 2018, 03:28
5
00:00

Difficulty:

85% (hard)

Question Stats:

41% (02:23) correct 59% (02:00) wrong based on 58 sessions

### HideShow timer Statistics

Q.In how many ways can 9 identical balls be distributed among four baskets such that each basket gets at least one ball?
A. 35
B. 56
C. 63
D. 70
E. 126
Please anybody solve this question and explain me how did you solve this question i am not able to do this question thanks in advance
CEO
Joined: 08 Jul 2010
Posts: 2537
Location: India
GMAT: INSIGHT
WE: Education (Education)
in how many ways can 9 identical balls be distributed among four baske  [#permalink]

### Show Tags

17 Mar 2018, 05:08
1
3
rishabhmishra wrote:
Q.In how many ways can 9 identical balls be distributed among four baskets such that each basket gets at least one ball?
A. 35
B. 56
C. 63
D. 70
E. 126
Please anybody solve this question and explain me how did you solve this question i am not able to do this question thanks in advance

This question is based on Distribution principle. It can be done in two ways

This is like find total Natural number solution of an equation a+b+c+d = 9

Method 1:

Natural Number solution of an equation in r variables = (n-1)C(r-1) = (9-1)C(4-1) = 8C3 = 56

Method 2:

Assign one ball to each basket i.e. 4 balls are gone and we are left with only 5 balls to assign to the baskets
Now every basket needs balls from 0 to 5
a+b+c+d = 5
and a, b, c and d may be any integer from 0 to 5
Now manually find solutions which is long but you get a pattern in that as well leading you to the answer i,e, 56

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3182
Location: India
GPA: 3.12
Re: in how many ways can 9 identical balls be distributed among four baske  [#permalink]

### Show Tags

17 Mar 2018, 12:20
1
1
rishabhmishra wrote:
Q.In how many ways can 9 identical balls be distributed among four baskets such that each basket gets at least one ball?
A. 35
B. 56
C. 63
D. 70
E. 126
Please anybody solve this question and explain me how did you solve this question i am not able to do this question thanks in advance

If we were to manually list down all the possibilities for the four baskets(and the 4 digit number is the total number of balls in the basket number one, two, three, and four)

6-1-1-1 (4 ways) - 6111,1611,1161,1116
3-2-2-2 (4 ways) - 3222,2322,2232,2223
4-2-2-1 (12 ways) - 4221,4212,4122,2124,2142,2421,2412,2241,2214,1224,1242,1422
4-3-1-1 (12 ways) - 4311,4131,4113,3411,3114,3141,1341,1431,1143,1134,1413,1314
1-2-3-3 (12 ways) - 1233,1323,1332,2133,2331,2313,3321,3231,3123,3132,3312,3213
5-1-1-2 (12 ways) - 5112,5121,5211,2511,2151,2115,1215,1251,1125,1152,1521,1512

Therefore, there are $$4*2 + 12*4$$ or 56 ways(Option B) in which the 9 balls can be arranged among the 4 baskets.
_________________

You've got what it takes, but it will take everything you've got

Math Expert
Joined: 02 Aug 2009
Posts: 6956
Re: in how many ways can 9 identical balls be distributed among four baske  [#permalink]

### Show Tags

17 Mar 2018, 22:45
rishabhmishra wrote:
Q.In how many ways can 9 identical balls be distributed among four baskets such that each basket gets at least one ball?
A. 35
B. 56
C. 63
D. 70
E. 126
Please anybody solve this question and explain me how did you solve this question i am not able to do this question thanks in advance

hi..

the question does NOT mention about the baskets, if they too are identical..
1) Identical boxes..
a) 6,1,1,1
b) 5,2,1,1
c) 4,3,1,1
d) 4,2,2,1
e) 3,3,2,1
f) 3,2,2,2
so 6 ways

2) non identical boxes..
a) 6,1,1,1 ............. $$\frac{4!}{3!} = 4$$
b) 5,2,1,1............. $$\frac{4!}{2!} = 4*3=12$$
c) 4,3,1,1............. $$\frac{4!}{2!} = 4*3=12$$
d) 4,2,2,1............. $$\frac{4!}{2!} = 4*3=12$$
e) 3,3,2,1............. $$\frac{4!}{2!} = 4*3=12$$
f) 3,2,2,2............. $$\frac{4!}{3!} = 4$$
so 4+12+12+12+12+4=56
In these cases we can take it as an equation a+b+c+d=9, as shown above..

For other type of such possible scenarios
https://gmatclub.com/forum/topic215915.html
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Senior Manager
Status: Countdown Begins...
Joined: 03 Jul 2016
Posts: 297
Location: India
Concentration: Technology, Strategy
Schools: IIMB
GMAT 1: 580 Q48 V22
GPA: 3.7
WE: Information Technology (Consulting)
Re: in how many ways can 9 identical balls be distributed among four baske  [#permalink]

### Show Tags

18 Mar 2018, 20:14
chetan2u

If we remove the last condition i.e. such that each basket gets at least one ball. The possible combination - 9!^4 am I correct?
Re: in how many ways can 9 identical balls be distributed among four baske &nbs [#permalink] 18 Mar 2018, 20:14
Display posts from previous: Sort by